The maker of the popular Beats by Dr. Dre headphones is looking to buy out its Asian partner and bring in a new investor that can provide it with fresh funds for growth, people familiar with the matter said.

The moves come as the founders of Beats Electronics LLC—music mogul Jimmy Iovine and American hip-hop producer and artist Andre Young, better known as Dr. Dre—are broadening the company's business from headphones to include...